We extend the previous example to include a co-primary endpoint relating to disability, a binary response defined as 75 (out of 100) or more on the short form-36 physical function subscale [1]}, where the mean score for the UK adult population is around 85. An in PACE, the endpoints will be analysed separately, each time fitting a logisitc mixed effect model and conducting a likelihood ratio test as described in Section REF . The results of the trial will be considered positive only if both of the analyses show a statistically significant difference, leading to reduced power under the alternative hypothesis of an effect on each endpoint in comparison to the univariate case of Section  REF[2]}. Correlation between the endpoints is expected at the participant level, and correlations between the random effects of therapists and doctors for different endpoints are also expected. This correlation will be modelled in the data generating process, but not in the analysis due to concerns about the feasibility of fitting a multivariate model. Such a mismatch between the data generating and analysis models has been noted as a clear motivation for simulation-based power calculations [3]}.
